## Optimal positioning in derivative securities (2001)

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Citations: | 7 - 0 self |

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@MISC{Carr01optimalpositioning,

author = {Peter Carr and Dilip Madan},

title = {Optimal positioning in derivative securities},

year = {2001}

}

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### Abstract

### Citations

1615 | Portfolio Selection - Markowitz - 1952 |

896 |
Optimum consumption and portfolio rules in a continuous-time model
- Merton
- 1971
(Show Context)
Citation Context ...ors to hold derivatives individually, even though derivatives are not held in aggregate. Optimal Positioning in Derivative Securities 1 Introduction The portfolio selection problem pioneered by Merton=-=[28]-=- generally does not consider derivative securities as potential investment vehicles. Similarly, the asset allocation approach favored by practitioners does not 1 consider derivatives as a distinct ass... |

376 |
Prices of State Contingent Claims Implicit in Options Prices
- Breeden, Litzenberger
- 1978
(Show Context)
Citation Context ...ure from reality. 2.2 Spanning It is well known that our market structure implies the existence of a unique risk-neutral density that may be identified from option prices (see Breeden and Litzenberger=-=[1]-=-). It is also well known that investors can achieve any smooth function of the underlying stock price by taking a static position at time 0 1 . However, the previous literature does not explicitly ide... |

323 |
Optimal consumption and portfolio policies when asset prices follow a diffusion process
- Cox, Huang
- 1989
(Show Context)
Citation Context ...s in these three asset classes are determined by the investors' preferences for risk, their probabilities of underlying returns, and by market prices of the three asset types. As in Pliska[30] and Cox=-=[7]-=-, we solve for these optimal positions by dividing the optimal investment problem into two sub-problems. The first sub-problem is to determine the optimal wealth profile as a function of the market pr... |

321 | A general version of the fundamental theorem of asset pricing, Mathematische Annalen 300 - Delbaen, Schachermayer - 1994 |

241 |
The Valuation of Uncertain Income Streams and the Pricing of Options
- Rubinstein
- 1976
(Show Context)
Citation Context ... 2 , v). (45) The requirement (19) that the stock's risk-neutral expected return be the riskfree rate implies that -v 2 = r, so that the Black Scholes formula holds for options, as shown in Rubinstein=-=[12]-=-. However, no one holds any options in this economy, as shown in (34). Returning to the case of heterogeneous lognormal beliefs, substituting (14) in (33) determines the optimal payo# in our present s... |

145 |
Foundations for Financial Economics
- Huang, Litzenberger
- 1988
(Show Context)
Citation Context ...nd V 0 [D i ] is the value of the payoff D i (S) j ln (p i (S)=q(S)): V 0 h e flD i i = B 0 Z 1 0 [p i (S)=q(S)] fl i q(S)dS V 0 [D i ] = B 0 Z 1 0 ln[p i (S)=q(S)]q(S)dS: 7 See Huang and Litzenberger=-=[23] pg.-=- 134 for example. 8 Integrating (16) once implies that LRT utility functions are positive linear transformations of: U i (W ) = 8 ! : 1 fl i \Gamma1 (�� i + fl i W ) 1\Gamma1=fl i ; if fl i 6= 1; ... |

128 |
A stochastic calculus model of continuous trading: Optimal portfolios
- Pliska
- 1986
(Show Context)
Citation Context ...l investment decision can be analyzed in a setting in which derivatives are absent. This is the viewpoint taken in the continuous-time analyses by Merton[28], Brennan, Lagnado, and Schwartz[4], Pliska=-=[31]-=-, and Cox and Huang[9]. Merton[28] derives the optimal consumption and portfolio policies by solving a nonlinear partial differential equation (p.d.e.) governing the utility of optimized wealth. Brenn... |

75 |
The Pricing of Contingent Claims in Discrete Time Models
- Brennan
- 1979
(Show Context)
Citation Context ...the risk-neutral density is given by: q(S) = # exp(-S/#)p(S). (53) Thus, if p(S) is normal, then q(S) is also normal with the same variance and with mean equal to the forward price as shown in Brennan=-=[2]-=-. The next subsection assumes that p is lognormal, and shows that q ends up 22 in a di#erent class than p. We also allow for heterogeneity in means and volatilities. 5.1 Zero Cautiousness and Lognorma... |

70 |
Arbitrage and Equilibrium in Economies with Inflnitely Many Commodities
- Kreps
(Show Context)
Citation Context ...om terminal wealth W i . Each investor's beliefs are characterized by a probability density function p i (S), defined on the entire positive half line with p i (S) ? 0 for S ? 5 For example, see Kreps=-=[26]-=-. 0. Each investor is assumed to maximize expected utility R 1 0 U(W i )p i (S)dS. Since all terminal wealth is consumed, W i can be replaced by a function f(S) relating terminal wealth to the termina... |

64 |
Who Should buy Portfolio Insurance
- Leland
- 1980
(Show Context)
Citation Context ...equires a model for determining optimal positions in derivative securities. Fortunately, some outstanding work has been done in this area, most notably the work of Brennan and Solanki[3] and of Leland=-=[9]-=-. This work shows for example that the conservative investor who believes volatility should be high should sell at-the-money options, but then protect against severe losses by buying out-of-the-money ... |

60 |
The Structure of Investor Preferences and Asset Returns, and Separability in Portfolio Allocation: A Contribution to the Pure Theory of Mutual Funds
- Cass, Stiglitz
- 1970
(Show Context)
Citation Context ...t all investors must have an increasing payo#. The greater the investor's risk tolerance relative to the total, the greater the exposure of the investor's position. 11 The results of Cass and Stiglitz=-=[4]-=- imply that investors with homogeneous beliefs and linear risk tolerances with identical cautiousness (i.e. T (W ) = # i + #W ) will not hold derivatives. This raises the question of sufficient condit... |

56 | A variational problem arising in financial economics - Cox, Huang - 1991 |

39 | Mean-variance theory in complete markets - Dybvig, Ingersoll - 1982 |

38 |
The strong case for the generalized logarithmic utility model as the premier model of financial markets
- Rubinstein
- 1978
(Show Context)
Citation Context ...) = ln(# i +W ), then marginal utility is: U # i (W ) = 1 # i +W , (27) and risk tolerance is linear with unitary cautiousness: T i [W i ] # - U # i (W ) U ## i (W ) = # i +W i . (28) 7 See Rubinstein=-=[13]-=- for further motivation for the use of this preference structure. 13 Substituting the inverse of the marginal utility function function (27) in (12), solving for #, and substituting in (9) implies 8 t... |

36 | Two-person dynamic equilibrium in the capital market
- Dumas
- 1989
(Show Context)
Citation Context ...of a positive constant and a squared linear position in the stock. Figure 2 graphs the optimal payo#s. Although the results of Corollary 3 pertain to only two investors, it is worth quoting from Dumas=-=[6]-=- 6 : The two-investor equilibrium is as basic to financial economics as is the two-body problem in mechanics. In order to obtain explicit solutions for the optimal payo# in an n investor economy, we n... |

35 | Martingale and Multiperiod Securities Markets - Harrison, Kreps - 1979 |

33 | Martingales and Stochastic - Harrison, Pliska - 1981 |

33 | Options and Efficiency - Ross - 1976 |

30 | On the consistency of the Black-Scholes model with a general equilibrium framework - Bick - 1987 |

27 |
Optimal portfolio insurance
- Brennan, Solanki
- 1981
(Show Context)
Citation Context ...of this problem requires a model for determining optimal positions in derivative securities. Fortunately, some outstanding work has been done in this area, most notably the work of Brennan and Solanki=-=[3]-=- and of Leland[9]. This work shows for example that the conservative investor who believes volatility should be high should sell at-the-money options, but then protect against severe losses by buying ... |

24 | Who buys and who sells options: The role of options in an economy with background risk
- Franke, Stapleton, et al.
- 1998
(Show Context)
Citation Context ...ure research should investigate more fully the relationship between the implications of heterogeneous beliefs and the consequences of background risk as studied in Franke, Stapleton, and Subrahmanyam =-=[7]-=-. For example, it would be interesting to investigate whether higher background risk corresponds to a larger e#ective volatility view held by an investor engaged in a buy and hold strategy. Other inte... |

23 | On viable diffusion price processes of the market portfolio - Bick - 1990 |

20 |
Requiem for A Market: An Analysis of the Rise and Fall of a Financial Futures Contract
- Johnston, McConnel
- 1989
(Show Context)
Citation Context ...19, 20], Breeden and Litzenberger[2], Friesen[16], Kreps[25], and Arditti and John[1]. A more recent stream discusses the optimal design of derivatives contracts. In particular, Johnston and McConnell=-=[24]-=-, and Duffie and Jackson[13] study the optimal design of futures contracts, while Brennan and Solanki[5] and Shimko[36] derive the optimal European-style payoff in a one period model for a single inve... |

17 | Spanning and completeness with options,” The
- Nachman
- 1988
(Show Context)
Citation Context ...+ f # (S 0 )S 0 + # S0 0 f ## (K)P 0 (K)dK + # # S0 f ## (K)C 0 (K)dK. (2) 1 This observation was first noted in Breeden and Litzenberger[1] and established formally in Green and Jarrow[8] and Nachman=-=[10]-=-. 2 An important special case of (1) is put-call-parity, which arises when f(S) is the payo# of an in-the-money call (S -K0 ) + for K0sS0 . In this case f # (S0 ) = 1, while f ## (K0 ) is a delta func... |

16 |
and R A Jarrow. Spanning and completeness in markets with contingent claims
- Green
- 1987
(Show Context)
Citation Context ...(S 0 )S 0 ]B 0 + f # (S 0 )S 0 + # S0 0 f ## (K)P 0 (K)dK + # # S0 f ## (K)C 0 (K)dK. (2) 1 This observation was first noted in Breeden and Litzenberger[1] and established formally in Green and Jarrow=-=[8]-=- and Nachman[10]. 2 An important special case of (1) is put-call-parity, which arises when f(S) is the payo# of an in-the-money call (S -K0 ) + for K0sS0 . In this case f # (S0 ) = 1, while f ## (K0 )... |

16 |
Multi-Period Securities and the Efficient Allocation of Risk: A Comment on the Black-Scholes Option Pricing Model
- Kreps
- 1982
(Show Context)
Citation Context ...achieved by introducing options into an economy. This literature was initiated by Ross[32], and received important contributions from Hakansson[19, 20], Breeden and Litzenberger[2], Friesen[16], Kreps=-=[25]-=-, and Arditti and John[1]. A more recent stream discusses the optimal design of derivatives contracts. In particular, Johnston and McConnell[24], and Duffie and Jackson[13] study the optimal design of... |

16 |
Mutual Fund Separation in Financial Theory-The Separating Distributions
- Ross
- 1978
(Show Context)
Citation Context ...old is that investors have linear risk tolerance (LRT): T i (W ) j \Gamma U 0 i (W ) U 00 i (W ) = �� i + fl i W: (14) 6 Working in a multi-asset setting with arbitrary concave utility functions, =-=Ross[33]-=- describes the distributional restrictions which are necessary and sufficient to generate two fund monetary separation. The parameter fl i is frequently called cautiousness in the literature 7 as it d... |

15 | Theory of Distributions - A Nontechnical Introduction - Richards, Youn - 1990 |

11 | Volatility trading. London Business School working paper - Neuberger - 1990 |

7 |
Option pricing theory and its applications
- Cox, Huang
- 1989
(Show Context)
Citation Context ...e lognormal risk-neutral density, V 0 [S # i S i ] = S # i S i 0 B 0 e # i S i (r-# 2 /2)+# 2 i S 2 i # 2 /2 . The optimality of this payo# in the continuous-time context is discussed in Cox and Huang=-=[5]-=-. Figure 1 shows the e#ect of varying the expected return on the optimal payo#. Whensi > r + # i # 2 (eg.s= 8.25%, the investor takes 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.5 1 1.5 2 2.5 3 Stock Pr... |

7 |
Spanning the State Space with Options
- Arditti, John
- 1980
(Show Context)
Citation Context ...tions into an economy. This literature was initiated by Ross[32], and received important contributions from Hakansson[19, 20], Breeden and Litzenberger[2], Friesen[16], Kreps[25], and Arditti and John=-=[1]-=-. A more recent stream discusses the optimal design of derivatives contracts. In particular, Johnston and McConnell[24], and Duffie and Jackson[13] study the optimal design of futures contracts, while... |

7 |
Welfare Aspects of Options and Supershares
- Hakansson
- 1978
(Show Context)
Citation Context ...o streams. An early stream focussed on the welfare gains achieved by introducing options into an economy. This literature was initiated by Ross[32], and received important contributions from Hakansson=-=[19, 20]-=-, Breeden and Litzenberger[2], Friesen[16], Kreps[25], and Arditti and John[1]. A more recent stream discusses the optimal design of derivatives contracts. In particular, Johnston and McConnell[24], a... |

6 |
A discrete time stochastic decision model
- Pliska
- 1982
(Show Context)
Citation Context ...mal positions in these three asset classes are determined by the investors' preferences for risk, their probabilities of underlying returns, and by market prices of the three asset types. As in Pliska=-=[30]-=- and Cox[7], we solve for these optimal positions by dividing the optimal investment problem into two sub-problems. The first sub-problem is to determine the optimal wealth profile as a function of th... |

6 | On the optimality of portfolio insurance - Benninga, Blume - 1985 |

5 | On Equilibrium Asset Price Processes,” Review of Financial Studies - He, Leland - 1993 |

4 |
Options and Efficiency", Quarterly
- Ross
- 1976
(Show Context)
Citation Context ...ted with other broad asset classes. Under this view, the introduction of derivatives enhances the investment possibility frontier. In fact, this paper extends a line of investigation initiated by Ross=-=[32]-=- in which derivatives complete the market. Working in a single period setting, we show how investors can determine 1 For example, three recent comprehensive texts on asset allocation are Gibson[17], V... |

3 |
Theory of Distributions: A Non-technical Introduction
- Richards, Youn
- 1990
(Show Context)
Citation Context ...-call-parity, which arises when f(S) is the payo# of an in-the-money call (S -K0 ) + for K0sS0 . In this case f # (S0 ) = 1, while f ## (K0 ) is a delta function centered at K0 . See Richards and Youn=-=[11]-=- for an accessible introduction to generalized functions such as delta functions. 3 We require that the payo# be twice di#erentiable and that the integrals in (2) not diverge. 4 Appendix 2 shows that ... |

3 |
Asset Allocation: Balancing Financial Risk
- Gibson
- 1996
(Show Context)
Citation Context ...oss[32] in which derivatives complete the market. Working in a single period setting, we show how investors can determine 1 For example, three recent comprehensive texts on asset allocation are Gibson=-=[17]-=-, Vince[38], or Leibowitz et. al.[27], none of which cover derivatives. 2 See Evnine and Hendriksson[15] and Tilley and Latainer[37] for discussions on the use of options in an asset allocation framew... |

3 |
The superfund: Efficient paths toward efficient capital markets in large and small countries
- Hakansson
- 1977
(Show Context)
Citation Context ...o streams. An early stream focussed on the welfare gains achieved by introducing options into an economy. This literature was initiated by Ross[32], and received important contributions from Hakansson=-=[19, 20]-=-, Breeden and Litzenberger[2], Friesen[16], Kreps[25], and Arditti and John[1]. A more recent stream discusses the optimal design of derivatives contracts. In particular, Johnston and McConnell[24], a... |

3 |
A Synthetic Option Framework for Asset Allocation" Financial Analysts Journal 41 (May/June 1985): 32-43. Reprinted as Chapter 12 of [64], 384-400. IV. Option Pricing by Esscher Transforms 87
- TILLEY, LATAINER
(Show Context)
Citation Context ...ple, three recent comprehensive texts on asset allocation are Gibson[17], Vince[38], or Leibowitz et. al.[27], none of which cover derivatives. 2 See Evnine and Hendriksson[15] and Tilley and Latainer=-=[37]-=- for discussions on the use of options in an asset allocation framework. their optimal investment in the riskless asset, a risky asset, and in options written on this risky asset. The optimal position... |

3 |
The New Money Management: A Framework for Asset Allocation
- Vince
- 1995
(Show Context)
Citation Context ...which derivatives complete the market. Working in a single period setting, we show how investors can determine 1 For example, three recent comprehensive texts on asset allocation are Gibson[17], Vince=-=[38]-=-, or Leibowitz et. al.[27], none of which cover derivatives. 2 See Evnine and Hendriksson[15] and Tilley and Latainer[37] for discussions on the use of options in an asset allocation framework. their ... |

3 | The Superfund: E#cientPaths Toward E#cient Capital - Hakansson - 1977 |

3 | Options and E#ciency", Quarterly - Ross - 1976 |

3 | A discrete time stochastic decision model Advances in Filtering and Optimal Stochastic Control ed - Pliska - 1982 |

2 |
Asset Allocation and Options
- Evnine, Henriksson
- 1987
(Show Context)
Citation Context ...ors can determine 1 For example, three recent comprehensive texts on asset allocation are Gibson[17], Vince[38], or Leibowitz et. al.[27], none of which cover derivatives. 2 See Evnine and Hendriksson=-=[15]-=- and Tilley and Latainer[37] for discussions on the use of options in an asset allocation framework. their optimal investment in the riskless asset, a risky asset, and in options written on this risky... |

2 |
The Arrow-Debreu model extended to financial markets
- FRIESEN
- 1979
(Show Context)
Citation Context ...fare gains achieved by introducing options into an economy. This literature was initiated by Ross[32], and received important contributions from Hakansson[19, 20], Breeden and Litzenberger[2], Friesen=-=[16]-=-, Kreps[25], and Arditti and John[1]. A more recent stream discusses the optimal design of derivatives contracts. In particular, Johnston and McConnell[24], and Duffie and Jackson[13] study the optima... |

2 | Chi-fu Huang(1989) Optimum consumption and portfolio policies when asset prices follw a diffusuion process Journal of Economic Theory - Cox |

2 | Asset Allocation: Balancing Financial Risk (2nd ed - Gibson - 1996 |

2 | Spanning and completeness with options Rev - Nachman - 1988 |